Quantum metrology in Lipkin-Meshkov-Glick critical systems

Giulio Salvatori, Antonio Mandarino, and Matteo G. A. Paris
Phys. Rev. A 90, 022111 – Published 15 August 2014

Abstract

The Lipkin-Meshkov-Glick (LMG) model describes critical systems with interaction beyond the first-neighbor approximation. Here we address quantum metrology in LMG systems and show how criticality may be exploited to improve precision. At first we focus on the characterization of LMG systems themselves, i.e., the estimation of anisotropy, and address the problem by considering the quantum Cramér-Rao bound. We evaluate the quantum Fisher information of small-size LMG chains made of N=2, 3, and 4 lattice sites and also analyze the same quantity in the thermodynamical limit. Our results show that criticality is indeed a resource and that the ultimate bounds to precision may be achieved by tuning the external field and measuring the total magnetization of the system. We then address the use of LMG systems as quantum thermometers and show that (i) precision is governed by the gap between the lowest energy levels of the systems and (ii) field-dependent level crossing is a metrological resource to extend the operating range of the quantum thermometer.

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  • Received 22 June 2014

DOI:https://doi.org/10.1103/PhysRevA.90.022111

©2014 American Physical Society

Authors & Affiliations

Giulio Salvatori and Antonio Mandarino

  • Dipartimento di Fisica, Università degli Studi di Milano, I-20133 Milan, Italy

Matteo G. A. Paris*

  • Dipartimento di Fisica, Università degli Studi di Milano, I-20133 Milan, Italy and CNISM, Udr Milano, I-20133 Milan, Italy

  • *matteo.paris@fisica.unimi.it

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Issue

Vol. 90, Iss. 2 — August 2014

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